COMPACT, a tutorial

Scott W. Williams

State University of New York in Buffalo

title and preface

page 1:
the beginnings

page 2:
a special example

functional separation

the universe in a box

open covers



the compact tutorial references

Alexandrov, P. and Urysohn, P. (1923) Sur les espaces topologiques compacts, Bull. Intern. Acad. Pol. Sci. Sér. A., 5-8.

Bolzano, B. Functionlehre, 1833-1841 (from Bolzano's manuscripts in Spisy B. Bolzana 1, Prague 1930.

Bolzano, B. Zahlenlehre, 1842 (from Bolzano's manuscripts in Spisy B. Bolzana 2, Prague 1931.

Cantor, G. (1883) Über unendliche lineare Punktmannigfaltigkiet, Math. Annalen 21, 51-58, 545-591.

Cech, E. (1937) On bicompact spaces, Annals of Math. 38, 823-844.

Fréchet, M. (1910) Les dimensions d'un ensemble abstrait, Math. Ann. 68, 145-168.

Hildebrandt, T. H. (1925) The Borel Theorem and its Generalizations. In J. C. Abbott (Ed.), The Chauvenet Papers: A collection of Prize-Winning Expository Papers in Mathematics. Mathematical Association of America.

Jarnik, V. (1981) Bolzano and the foundations of mathematical analysis, Society of Czechoslovak Mathematicians and Physicists.

Kline, M. (1972) Mathematical Thought: From Ancient to Modern Times. Oxford University Press.

Lawrence, L. B. (1996) Failure of normality in the box product of uncountably many real lines. Trans. Amer. Math. Soc. 348, no. 1, 187--203.

Rudin, M.E. (1972) The box product of countably many compact metric spaces, Gen. Top. Appl. 2, 293-248.

Taylor, A. (1982). A Study of Maurice Fréchet: I. His Early Work on Point Set Theory and the Theory of Functionals. Archive for History of Exact Sciences, 27 (3), 233-295.

Taylor, A. (1985). A Study of Maurice Fréchet: II. Mainly about his Work on General Topology 1909-1928. Archive for History of Exact Sciences 34 (3), 279-380.

Tietze, H. (1923). Beitrage zur allgemeinen topologie I, Math. Ann. 88, 280-312.

Tychonov, A. (1930). Über die topologische Erweiterung von Räume, Math. Ann. 102, 544-561.

Vietoris, L. (1921). Stetige Mengen, Monatsh. für Math. und Phys. 31, 173-204.

Williams, S. (1984), Box products, Handbook of Set-Theoretic Topology (K. Kunen and J.E.Vaughan ed.), North-Holland, 169-200.

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